index-set

Index set

In mathematics, the elements of a setA may be indexed or labeled by means of a set J that is on that account called an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.

In complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set.

Examples

An enumeration of a set S gives an index set J sub mathbb{N}, where f:J rarr mathbb{N} is the particular enumeration of S.